AERODYNAMICS: WHITCOMB AREA RULE

Area rule

Whitcomb area rule

The Whitcomb area rule
(sometimes just called the area rule) is a design technique used to reduce an aircraft’s drag at transonic and supersonic speeds, particularly between Mach 0.8 and 1.2. This is the operating speed range of the
vast majority of all commercial and military fixed-wing aircraft today.

(Junkers patent drawing from March 1944.

The F-106 Delta Dart, a development of the F-102,
clearly shows the "wasp-waisted" shaping due to area rule considerations.

Oilflow visualization of flow separation without and with antishock bodies.

This F-5E, the Shaped
Sonic Boom Demonstrator, was modified by NASA
applying the areal rule at the fuselage below the wing to decrease the shock by the wings
and produce negative lift. Note that the wings still produce a shock due to compression lift, so the nose-cone is widened to produce an even stronger shock, which
therefor travels faster.)

To generate lift a supersonic airplane has to produce at least two shock waves: One over-pressure downwards wave, and one
under-pressure upwards wave. Whitcombs area rule states that air displacement can be
reused without generating additional shock waves. In this case the fuselage reuses some
displacement of the wings.

The Whitcomb area rule (sometimes just called the area rule) is a design
technique used to reduce an aircraft’s drag at transonic
and supersonic speeds, particularly between Mach 0.8 and 1.2. This is the operating
speed range of the vast majority of all commercial and military fixed-wing aircraft today.

Even at high subsonic speeds, local supersonic flow can develop in areas where the flow
accelerates around the aircraft body and wings due to Bernoulli’s principle. The speed at which this
occurs varies from aircraft to aircraft, and is known as critical mach. The resulting shock waves formed at these points of supersonic flow bleed
away a considerable amount of power, which is experienced by the aircraft as a sudden and
very powerful form of drag, called wave drag. In order to
reduce the number and power of these shock waves, the aircraft’s shape should change in
cross-sectional area as smoothly as possible. The design implications for standard
"tube and wing" aircraft are that the body narrows beside the wings. This leads
to a "perfect" aerodynamic shape known as the Sears-Haack body, roughly
shaped like a cigar but pointed at both ends.

The area rule was first discovered by a team including Heinrich
Hertel and Otto Frenzl
working on a transonic wind tunnel at Junkers works between 1943 and 1945; it is used in a patent filed
in 1944. The design concept was applied to a variety of German
wartime aircraft, including a rather odd Messerschmitt
project, but their complex double-boom design was never built even to the extent of a
model. Several other researchers came close to developing a similar theory, notably Dietrich Küchemann who designed a tapered fighter
that was dubbed the Küchemann Coke Bottle when it was discovered by US forces in 1946. In this case Küchemann arrived at
the solution by studying airflow, notably spanwise flow, over a swept wing.

Richard Whitcomb, after whom the rule is named,
independently discovered this rule in 1952, while working at NACA. While using the new
Eight-Foot High-Speed Tunnel, a wind tunnel with
performance up to Mach 0.95 at NACA’s Langley
Research Center, he was surprised by the increase in drag due to shock wave formation.The shocks could be seen using Schlieren photography, but the reason they were being created at speeds far below the
speed of sound, sometimes as low as Mach 0.70, remained something of a mystery.

In late 1951 the lab hosted a talk by Adolf Busemann,
a world-famous German aerodynamicist who had moved to Langley
after World War II. He talked about the difference in the
behaviour of airflow at speeds approaching the supersonic, where it no longer behaved as acompressible fluid. Whereas engineers were used to
thinking of air flowing smoothly around the body of the aircraft, at high speeds it simply
didn’t have time to "get out of the way", and instead started to flow as if it
were rigid pipes of flow, a concept Busemann referred to as "streampipes", as
opposed to streamlines, and jokingly suggested that
engineers had to consider themselves "pipefitters".

Several days later Whitcomb had a "Eureka!" moment. The reason for the high
drag was that the "pipes" of air were interfering with each other in three
dimensions. You could not simply consider the air flowing over a 2D cross-section of the
aircraft as you could in the past; now you also had to consider the air to the
"sides" of the aircraft which would also interact with these streampipes. Whitcomb realized that the Sears-Haack shaping had to apply tothe aircraft as a whole, rather
than just the fuselage. That meant that the extra cross sectional
area of the wings and tail had to be accounted for in the overall shaping, and that the
fuselage should actually be narrowed where they meet to more closely match the ideal.

The area rule was immediately applied to a number of development efforts. One of the
most famous was Whitcomb’s personal work on the re-design of the F-102 Delta Dagger, which was demonstrating
performance considerably worse than expected. By indenting the fuselage beside the wings,
and (paradoxically) adding more volume to the rear of the plane, transonic drag was
considerably reduced and the original Mach 1.2 design speeds were reached.

Numerous designs of the era were likewise modified in this fashion, or by adding new
fuel tanks or tail extensions to smooth out the profile. The Tupolev
Tu-95, a Soviet-era bomber,
was modified by adding large bulged nacelles behind its four engines, instead of
decreasing the cross section of the fuselage next to the wing root. It remains the highest
speed propeller aircraft in the world. The Convair 990 used a similar solution, adding bumps called
antishock bodies to the trailing edge of the upper wing. The 990 remains the fastest US airliner in history, cruising at up to Mach 0.89. Designers at Armstrong-Whitworth
took the concept a step further in their proposed M-Wing, in which the wing was first
swept forward and then to the rear. This allowed the fuselage to be narrowed on either
side of the root instead of just behind it, leading to a smoother fuselage that remained
wider on average than one using a classic swept wing.

One interesting outcome of the area rule is the current shaping of the Boeing 747‘s upper deck. The aircraft was originally designed
to carry standard cargo containers in a two-wide, two-high stack on the main deck, which
was considered a serious accident risk for the pilots if they were located in a cockpit at
the front of the aircraft. They were instead moved above the deck in a small
"pod", which was deliberately designed to be as small as possible given normal
streamlining principles. It was later realized that the drag could be reduced much more by
lengthening the pod, using it to reduce wave drag offsetting the tail surface’s
contribution. The new design was introduced on the 747-300, improving its cruise speed and
lowering drag.

Aircraft designed according to Whitcomb’s area rule looked odd at the time they were
first tested, (e.g. the Blackburn Buccaneer), and
were dubbed "flying Coke bottles," but the area rule is effective and came to be
an expected part of the appearance of any transonic vehicle. Later designs started with
the area rule in mind, and came to look much more pleasing. Although the rule still
applies, the visible fuselage "waisting" can only be seen on the B-1 Lancer ("the Bone") and the Tupolev Tu-160  the same effect is now achieved by
careful positioning of aircraft components, like the boosters and cargo bay of rockets,
the jet engines in front (and not below) the wings of a Airbus A380, the jet engines behind (and not purely at the
side) the fuselage of a Cessna Citation X , the
canopy of the F-22 Raptor, and this
image of the Airbus A380 in flight shows obvious area
rule shaping at the wing root, but these modifications are practically invisible from any
other angle. Aftershock bodies are likewise "invisible" today, serving double
duty as flap actuators, which also visible in the A380 image above.

The National Advisory Committee for Aeronautics
(NACA) was a U.S. federal agency
founded on March 3, 1915 to
undertake, promote, and institutionalize aeronautical research. On October 1, 1958 the agency was
dissolved, and its assets and personnel formed the core of the newly created National Aeronautics and Space Administration (NASA). NACA was
pronounced ‘En Ay Cee Ay’ rather than ‘Nakka’, and the name remains familiar in the
automotive world for the NACA duct, a form of air
intake, or to those in the aircraft industry, as several series of NACA-developed airfoils are still being used in new design.

NACA began as an emergency measure during World War I
to promote industry/academic/government coordination on war-related projects. By the early
1920s, it had adopted a new and more ambitious mission: to promote military and civilian
aviation through applied research that looked beyond current needs. NACA’s researchers
pursued this mission through the agency’s impressive collection of in-house wind tunnels,
engine test stands, and flight test facilities. Commercial and military clients were also
permitted to use NACA’s facilities on a contract basis.

In 1922, NACA had 100 employees. By 1938, it had 426. In addition to formal
assignments, staff were encouraged to pursue unauthorized "bootleg" research,
provided that is was not too exotic. The result was a long string of fundamental
breakthroughs, including "NACA engine cowl"
(1930s), the "NACA wing" (1940s), and the "area rule" for supersonic
aircraft (1950s). NACA claims credit for having the 1st aircraft to break the sound
barrier. They also claim credit for the 1st aircraft that eventually flew to the
"edge of space".

The NACA experience provided a powerful model for World
War II research, the postwar government laboratories, and NACA’s successor: the
National Aeronautics and Space Administration (NASA).